Method for characterising or controlling the production of a thin-layered component using optical methods

ABSTRACT

A method for characterizing or controlling the production of a thin-layered component using optical methods. Acquired signals S 1  and S 2  are processed in order to obtain parameters x, ε of the deposited layers. The stacking is represented by the product of two Abeles matrices for each direction of polarisation s (perpendicular to the incidence plane) and p (parallel to the incidence plane): a known matrix Mo s,p  representing the support and matrix dM s,p  representing a thin transparent layer being deposited. The signal variations measured, dS 1  and dS 2 , are inverted to obtain thickness x and dielectric constant ε of the thin layer by the following operations: Taylor expansion as a function of variation dx of thickness x of the thin layer of the coefficients of matrix dM; the coefficients of matrix M s,p  are calculated each in the form A(ε ±2 )dx 2 +B(ε ±1 )dx+C and the relation S 1,2 =A 1,2 (ε ±2 ) dx 2 +B 1,2 (ε ±1 ) dx+C 1,2  is thereby deduced which connects signals S 1  and S 2  to parameters ε and dx; dx is eliminated and a master function p(ε ±4 )=0 is thereby deduced; the equation is solved and the solutions are selected corresponding to values that are physically plausible in order to measure ε and use the ε value obtained to determine dx.

[0001] The present invention relates to a characterisation or controlmethod for preparation of a thin layer component by optical methods.

[0002] For the production of high quality optical layers, increasedcontrol of the preparation of each layer and of its refraction index hasbecome a crucial challenge. Among the different control method, it iswell known that ellipsometry is one of the most sensitive. It hastherefore been contemplated to compare in real time the evolution ofellipsometric parameters I_(s), I_(c), or any other combination of theseparameters with respect to a theoretical evolution.

[0003] It has been suggested to compare the distance between pointswhich are respectively theoretical and measured, represented in areferential I_(s), I_(c) or still the lengths of the travelled pathsmeasured.

[0004] It is, moreover, useful to have a reliable method forcharacterising the optical layers deposited. Then two possible aspectsshould be considered according to the usage made of the characterisationmethod. A dynamic aspect where after each new layer deposited ofthickness dx, the layers deposited are characterised by measuring forinstance optical signals S₁ and S₂. These signals enable then to get forinstance the control parameter ε of the layers deposited. ε is thedielectric constant of the layer with ε=n² where n is the optical index.If ε is equal to the value ε′ required, the following layer is depositedwithout re-adjusting the deposition parameters. Failing which, saidparameters are adjusted in order to correct the error. The depositionparameters may thus be corrected in real time for optimised control ofthe deposition.

[0005] Such a method may also be used to characterise the evolution ofthe refraction index in relation to deposition parameters, withoutimplementing any control of deposition. With reference to the fitting ofthe curve providing the variations of the dielectric constant ε as afunction of these parameters, the parameters necessary to the productionof a layer with a given index can be found. Such characterisation thusenables to minimise the number of cycles of deposition/characterisationnecessary for the production of a layer with a given index.

[0006] Various direct digital reversal methods have thus been developed,but have prove suitable only for relatively thick films (200-500 Å).Others, based fitting methods seem more efficient, but have thedisadvantage of requiring-tedious calculations and correction methods inorder to stabilise the variation of the refraction index.

[0007] Approximations have however been suggested in order to simplifythese calculations. It may be judicious, for instance, to reduce thenumber of parameters necessary to the fitting (“dispersion laws” [HeitzT and al.; J. Vac. Sci. Technol. A 18 (2000) 1303-1307], “Effectivemedium approximations” [Kildemo and al.; Applied Optics 37 (1998),5145-5149]) or reduce, using suitable optical approximations theproblems encountered when calculating the optical film (WKBJ, multipleintegral methods, etc. [Kildemo and al.; Applied Optics 37, (1998)113-124]).

[0008] However, these methods are too complex to be implemented in realtime and in various situations such as those which are indeedencountered when producing the stacks of layers.

[0009] Besides, polynomial methods are known for reversing theellipsometric signal [Lekner, J and al.; Applied Optics 33 (1994)5159-5165; Drolet, J. P. and al.; Opt. Soc. Am. A 11 (1994) 3284-329].These methods are, nevertheless, applicable only to non-absorbentmonolayer and to samples exhibiting very simple structures. They use,moreover, the ellipsometric angles Ψ and Δ as input parameters for thereversal formulae. Still, these values cannot be obtained directly bymost ellipsometers.

[0010] The purpose of the invention consists thus in providing acharacterisation or control method of the preparation of a componentmade of thin layers which is based on a direct reversal principle,enabling to access the physical parameters of the layer (its thickness xand its dielectric constant ε) in real time using the parametersmeasured in real time by an optical instrument.

[0011] This requires an approach and approximations which are part ofthe invention.

[0012] In this view, the invention relates to a characterisation orcontrol method for preparation of a thin layer component according tooptical methods wherein:

[0013] the parameters S₁ and S₂ related to the thickness x and to thecomplex optical index of the component are measured and acquired for atleast a wavelength λ,

[0014] the signals S₁ and S₂ thus acquired are processed in order toobtain the parameters x, ε of the layers deposited.

[0015] According to the invention:

[0016] the stacking is represented by the product of two Abeles matricesfor each polarisation direction s (perpendicular to the plane ofincidence) and p (parallel to the plane of incidence):

[0017] a matrix Mos_(s,p) known representing the support,

[0018] a matrix dm_(s,p) representing a thin transparent layer beingdeposited,

[0019] reversing the variations of the measured signals dS₁, dS₂ enablesto get the thickness x and the dielectric constant ε of the thin layerusing the following operations:

[0020] Taylor development in relation to the variation dx of thethickness x of the thin layer of the coefficients of the matrix dM,

[0021] calculating the coefficients of the matrix M_(s,p) each in theform

A(ε^(±2))dx²+B(ε^(±1))dx+C

[0022]  deducing therefrom the relation

S _(1,2) =A _(1,2)(ε^(±2))dx ² +B _(1,2)(ε^(±1))dx+C _(1,2)

[0023] linking the signals S₁ and S₂ to the parameters ε and dx,

[0024] eliminating dx

[0025] deducing therefrom a master function

p(±^(±4))=0

[0026]  solving the equation using an appropriate method,

[0027] selecting the solutions of this equation corresponding to valuesphysically plausible, to measure ε,

[0028] using the value ε obtained to determine dx.

[0029] The present invention also relates to the features which willappear during the following description and which should be consideredindividually or in all their technically possible combinations:

[0030] the Taylor development is limited to the second order,

[0031] said method is applied during the deposition of the stacking andthe evolution of ε and/or x_(o) is recorded,

[0032] said method is applied during the deposition of the stacking andthe conditions of the deposition are influenced to interlock theparameters ε, x of the layers with preset theoretical values,

[0033] the ellipsometer is phase-modulated generating the parametersI_(s) and I_(c),

[0034] the ellipsometer is fitted with a rotary polariser generating theparameters tan Ψ, cos Δ,

[0035] the thin layer is transparent,

[0036] the thin layer is absorbent,

[0037] the measurement is multiwavelength,

[0038] the thickness is optimised by averaging over the differentwavelengths,

[0039] after optimising the thickness, the complex indices arerecalculated,

[0040] if one of the measured signals S₁, S₂ is unusable, the other ofthe terms S1, S2 is developed to the second order in relation to time inthe relation S₁, S₂=A_(1,2)(ε^(±2))dx²+B_(1,2)(ε^(±1))dx+C_(1,2) inorder to determine a new master function P(ε^(±2))=0,

[0041] if the deposition rate in the initial conditions of deposition isunknown or is not constant during the deposition, the value of thereversing pitch is adapted dynamically,

[0042] for a film exhibiting a low absorption rate, attempt is made tominimise the deviation between required and reconstructed theoreticalvalues,

[0043] if no value is obtained for a given wavelength λ, the values ofthe indices ε obtained are processed statistically for variouswavelengths close to λ to deduce therefrom the value of ε for thewavelength λ considered.

[0044] The invention will be illustrated with reference to the appendeddrawings whereon the results are compared for the reconstruction ofreflection index profiles during plasma deposition:

[0045]FIG. 1 represents the evolution of the molecular oxygen flux andof the refraction index reconstructed as a function of the depositiontime for two different wavelengths;

[0046]FIG. 2 represents the variation of the refraction index as afunction of the molecular oxygen flux for two different wavelengths,

[0047]FIG. 3 represents the variation of the refraction index as afunction of the thickness for two different wavelengths. The symbolscorrespond to the values reconstructed according to the present methodand the lines are spectroscopic fittings;

[0048]FIG. 4 is a comparison of the ellipsometric intensities I_(s) andI_(c) obtained, either by measurements (symbols), or by spectroscopicfitting (solid line).

[0049] It is known that the optical response of a layer i to apolarisation light excitation, respectively s and p, may be representedby two matrices, so-called “Abeles matrices”M_(i), the thickness of thelayer being x and its complex index ε_(i) [Abeles, F.; Annales ofPhysique 5 (1950) 596-640; 706-782].

[0050] The Abeles matrix has then the following form:$M_{i} = \begin{pmatrix}{\cos \quad \phi_{i}} & {\frac{i}{q_{i}}\sin \quad \phi_{i}} \\{{iq}_{i}\quad \sin \quad \phi_{i}} & {\cos \quad \phi_{i}}\end{pmatrix}$

[0051] where φ_(i)=k{square root}{square root over (ε_(i)−α²)}x_(i),k=2π/λ being the wave number.

[0052] For the polarisation s (perpendicular to the plane of incidence)${q_{i} = \frac{ɛ_{i}}{\sqrt{ɛ_{i} - \alpha^{2}}}},$

[0053] for the polarisation p (parallel to the plane of incidence)q_(i)={square root}{square root over (ε_(i)−α²)}={haeck over (n)}_(i)cos γ_(i) where γ_(i) is the angle of propagation in the layer i.

[0054] α is linked to the dielectric constant ε and to the angle ofincidence γ_(i) by the following formula:

α={square root}{square root over (ε_(a))} sin γ_(a)={square root}{squareroot over (ε_(i))} sin γ_(i)

[0055] where a and i signify respectively “ambient” and “layer i”.

[0056] The optical response of the whole multilayer stacking isrepresented by the matrix M, product of the individual matricesrepresentative of each layer: $\begin{matrix}{M = {\begin{pmatrix}m_{11} & m_{12} \\m_{21} & m_{22}\end{pmatrix} = {\prod\limits_{i = 1}^{n}\quad M_{i}}}} & (1)\end{matrix}$

[0057] Finally, the Fresnel reflection coefficients (and similarly, thetransmission coefficients) of the stacking may be calculated as follows:$\begin{matrix}{r = \frac{{q_{a}m_{11}} - {q_{s}m_{22}} + {q_{a}q_{s}m_{12}} - m_{21}}{{q_{a}m_{11}} + {q_{s}m_{22}} + {q_{a}q_{s}m_{12}} + m_{21}}} & (2)\end{matrix}$

[0058] where a and s signify respectively “ambient” and “substrate”.

[0059] The method suggested according to the invention is based on thepolynomial development of the coefficients of the Abeles transfermatrices for a layer deposited i. This digital reversal method, unlikeprevious polynomial methods, is not limited to a single layer i. It may,indeed, be used iteratively for characterisation of the multilayer filmsif the Abeles matrices M of the stacking of the layers whereon the layeri has been deposited, are known or if they may have been reconstructedaccording to the formula mentioned in (1).

[0060] The method, according to the invention, may be applied quitegenerally to any optical signal used in situ for controlling thedeposition of thin layers. The optical signals S₁ and S₂ may then bederived from ellipsometric or photometric measurements as long as theyconsist of combinations of the complex Fresnel coefficients ofreflection or transmission.

[0061] In the case of ellipsometric measurements, one may wish todetermine the ratio$\rho = {\frac{r_{p}}{r_{s}} = {\tan \quad {\Psi }^{i\quad \Delta}}}$

[0062] where r_(p) and r_(s) are the complex Fresnel coefficients.

[0063] It is then known that these parameters may be obtained bydifferent types of measurements. The optical signals S₁ and S₂ measuredmay then be in relation to the optical instrument used, the followingparameters: Signal Signal Optical instrument S1 S2 Ellipsometry(ellipsometric angles) ψ Δ Phase-modulated ellipsometry Is IcEllipsometry with rotating analyser tan ψ cos Δ Ellipsometry withrotating analyser and tan ψ sin Δ compensator Reflectometry with obliqueangle of incidence R_(p) = r_(p).r_(p)* R_(s) = r_(s).r_(s)*

[0064] Thus, for instance, in phase-modulated ellipsometry, in theconfiguration II the following measurements are made—when the modulatoris oriented to 0°, the analyser to 45° and the angle between thepolariser and the modulator is set to 45° [Drévillon B. Prog. Cryst.Growth Charact. Matter 27 (1993),1]:$I_{s} = {{\sin \quad 2{\psi sin}\quad \Delta} = {2\quad {{Im}\left( \frac{r_{s}^{*}r_{p}}{{r_{s}r_{s}^{*}} + {r_{p}r_{p}^{*}}} \right)}}}$$I_{c} = {{\sin \quad 2\psi \quad \cos \quad \Delta} = {2\quad {{Re}\left( \frac{r_{s}^{*}r_{p}}{{r_{s}r_{s}^{*}} + {r_{p}r_{p}^{*}}} \right)}}}$

[0065] which correspond to the first and second harmonics of thepolarised light.

[0066] In the particular case of transparent layers on a substrate whichis thick (>0,1 μm) and transparent, the reflection of the rear face ofthe substrate should be taken into consideration. In such a case, thephase coherence of the incident light is lost and depolarisationphenomena take place. Then, r_(s,p)*r_(s,p) should be replaced withproducts averaged along the optical path [Kildemo and al.; Thin Solidfims 313 (1998),108] $\begin{matrix}{{\langle{r_{s,p}r_{s,p}^{*}}\rangle} = {{r_{s,p}r_{s,p}^{*}} + \frac{\left( {t_{s,p}t_{s,p}^{*}} \right)\left( {t_{s,p}^{\prime}t_{s,p}^{\prime*}} \right)\left( {r_{{bs},p}r_{{bs},p}^{*}} \right)^{{- 4}\quad {Im}\quad \beta_{s}}}{1 - {\left( {r_{{bs},p}^{\prime}r_{{bs},p}^{\prime}} \right)\left( {r_{{bs},p}r_{{bs},p}^{*}} \right)^{{- 4}\quad {Im}\quad \beta_{s}}}}}} & (3)\end{matrix}$

[0067] where β_(s) is equal to${2\pi \frac{x_{s}}{\lambda}\sqrt{ɛ_{s}^{2} - {ɛ_{a}^{2}\sin^{2}\phi_{a}}}},$

[0068] (t_(s,p)) and (t′_(s,p)) are the transmission Fresnelcoefficients of the stacking of layers, respectively in one directionand in the other and x_(s) and ε_(s) ar the thickness and the dielectricconstant of the substrate, a signifies “ambient”.

[0069] In the case of a thin surface layer, whereof the thickness is dx,it is represented by the Abeles matrices dMs and dMp, respectively forthe directions s and p of the incident polarisation, according to thefollowing formulae: $\begin{matrix}{{dMs} = \begin{bmatrix}{{\cos \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}\quad} & {\frac{i}{\sqrt{ɛ - \alpha^{2}}} \cdot {\sin \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}} \\{i \cdot \sqrt{ɛ - \alpha^{2}} \cdot {\sin \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}} & {\cos \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}\end{bmatrix}} & (4) \\{{dMp} = \begin{bmatrix}{{\cos \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}\quad} & {i \cdot \frac{\sqrt{ɛ - \alpha^{2}}}{ɛ} \cdot {\sin \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}} \\{i \cdot \frac{ɛ}{\sqrt{ɛ - \alpha^{2}}} \cdot {\sin \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}} & {\cos \left( {k{\sqrt{ɛ - \alpha^{2}} \cdot {x}}} \right)}\end{bmatrix}} & (5)\end{matrix}$

[0070] According to the invention, it is suggested to proceed to aTaylor development on the coefficients of these matrices, for instanceof the second order, enabling to obtain: $\begin{matrix}{{dMs} = \begin{bmatrix}{{1 + {\left\lbrack {\frac{- 1}{2} \cdot k^{2} \cdot \left( {ɛ - \alpha^{2}} \right)} \right\rbrack \cdot {x^{2}}}}\quad} & {{i \cdot k \cdot {x}}\quad} \\{{i \cdot \left( {ɛ - \alpha^{2}} \right) \cdot k \cdot {x}}\quad} & {1 + {\left\lbrack {\frac{- 1}{2} \cdot k^{2} \cdot \left( {ɛ - \alpha^{2}} \right)} \right\rbrack \cdot {x^{2}}}}\end{bmatrix}} & (6) \\{{dMp} = \begin{bmatrix}{{1 + {\left\lbrack {\frac{- 1}{2} \cdot k^{2} \cdot \left( {ɛ - \alpha^{2}} \right)} \right\rbrack \cdot {x^{2}}}}\quad} & {\quad {i \cdot \left( {1 - {\frac{1}{ɛ} \cdot {\alpha 2}}} \right) \cdot k \cdot {x}}} \\{{i \cdot ɛ \cdot k \cdot {x}}\quad} & {1 + {\left\lbrack {\frac{- 1}{2} \cdot k^{2} \cdot \left( {ɛ - \alpha^{2}} \right)} \right\rbrack \cdot {x^{2}}}}\end{bmatrix}} & (7)\end{matrix}$

[0071] It appears thus that the different coefficients of these matricesare in the form:

A(ε^(±2))·dx²+B(ε^(±1))·dx+C  (8)

[0072] where A(ε^(±2)) and B(ε^(±1)) are polynomials of ε as follows:$\begin{matrix}{{B\left( ɛ^{\pm 1} \right)} = {{C_{1}^{B}ɛ} + C_{0}^{B} + \frac{C_{- 1}^{B}}{ɛ}}} & (9) \\{{A\left( ɛ^{\pm 2} \right)} = {{C_{2}^{A}ɛ^{2}} + {C_{1}^{A}ɛ} + C_{0}^{A} + \frac{C_{- 1}^{A}}{ɛ} + \frac{C_{- 2}^{A}}{ɛ^{2}}}} & (10)\end{matrix}$

[0073] where C_(i) ^(A,B) are complex constants.

[0074] When the previous measurement(s) enable to access (or toreconstruct) digitally the coefficients of the matrices Ms, Mp, one maydeduce therefrom (by simple matrix multiplication) the coefficients ofthe polynomials A and B of the matrices produced

M _(s) ^(prod) =dMs·Ms, M _(p) ^(prod) =dMp·Mp

[0075] To then extract the reflection Fresnel coefficients as a functionof ε and dx, the coefficients of the matrices M_(s,p) ^(prod) in theformulae mentioned above (2) should be replaced.

[0076] The equations are obtained as follows:$r_{s,p}^{prod} = \frac{{{A\left( ɛ^{\pm 2} \right)}{x^{2}}} + {{B\left( ɛ^{\pm 1} \right)}{x}} + C}{{{A^{\prime}\left( ɛ^{\pm 2} \right)}{x^{2}}} + {{B^{\prime}\left( ɛ^{\pm 1} \right)}{x}} + C^{\prime}}$

[0077] By dividing these polynomials and by keeping only the terms ofthe second order, an expression as follows can be obtained:

r _(s,p) ^(prod) ≈r _(s,p) +dr _(s,p) =C+A(ε^(±2))·dx ²+B(ε^(±1))·dx  (11)

[0078] where r_(s,p) are the reflection coefficients of the stackingbefore the layer being deposited and dr_(s,p) represents the changes inthe reflection properties introduced by this layer being deposited.

[0079] It may then be noticed that C is identical to r_(s,p) which isthe reflection coefficient of the stacking before deposition of the lastlayer.

[0080] To link these formulae to the optical parameters measured, S₁ andS₂, one should introduce the coefficients of these polynomials in one ofthe equations mentioned according to the type of measurements defined onthe table of page 7.

[0081] By using suitable formulae, one may finally express the signalmeasured in relation to dx, dx² and of polynomials depending essentiallyon ε:

dS ₁ =A ₁(ε^(±2)).dx ² +B ₁(ε^(±1)).dx  (12)

dS ₂ =A ₂(ε^(±2)).dx ² +B ₂(ε^(±1)).dx  (13)

[0082] which is simple in the case of transparent materials ε_(i)=0.

[0083] When dS₁ and dS₂ are known experimentally, it is possible tointroduce them in the previous equations and dx may be expressed in twodifferent ways in relation to polynomials of ε: $\begin{matrix}{{dx}_{1} = {\frac{{{dS}_{1} \cdot B_{2}} - {{dS}_{2} \cdot B_{1}}}{{{dS}_{2} \cdot A_{1}} - {{dS}_{1} \cdot A_{2}}} = \frac{T\left( ɛ^{\pm 1} \right)}{T_{2}\left( ɛ^{\pm 2} \right)}}} & (14) \\{{dx}_{2} = {\frac{{{dS}_{2} \cdot A_{1}} - {{dS}_{1} \cdot A_{2}}}{{B_{2} \cdot A_{1}} - {B_{1} \cdot A_{2}}} = \frac{T\left( ɛ^{\pm^{2}} \right)}{T_{2}\left( ɛ^{\pm 3} \right)}}} & (15)\end{matrix}$

[0084] Both these thicknesses being identical by definition, one has thefollowing relation which the dielectric function must verify:

P(ε^(±4))=T(ε^(±2))² =T ₁(ε^(±1))·T ₂(ε^(±3))=0  (16)

[0085] The latter function is called “master function”. This function isthen multiplied by ε⁴ in order to obtain a polynomial equation of order8. This equation is then solved and the solutions are filtered with aview to keeping only the solutions which are physically significant. Todo so, the solutions without any physical direction are eliminated sinceε should be real and strictly greater than 1. Moreover, the thickness dxcalculated using ε should be positive and the optical thickness shouldbe smaller than λ/4. Finally, among the remaining solutions, thesolution whereof the value is closest to experimental value is selected.To do so, for the different solutions a criterion σ² is determined:$\begin{matrix}{\sigma^{2} = {\frac{\left( {{dS}_{1}^{\prime} - {dS}_{1}} \right)^{2}}{\Delta \quad S_{1}^{\quad 2}} + \frac{\left( {{dS}_{2}^{\prime} - {dS}_{2}} \right)^{2}}{\Delta \quad S_{2}^{2}}}} & (17)\end{matrix}$

[0086] where dS′_(1,2) is the value calculated using ε, dxreconstructed, dS_(1,2) are the experimental values and ΔS_(1,2) theerrors on the measurement.

[0087] The solution with the smallest σ² is selected.

[0088] Once ε determined, the value obtained in the equation (14) isinjected in order to obtain the thickness dx.

[0089] Acquisition of the measurement at different wavelengths enablesto impose the complementary condition according to which the thicknessof the new layer must be equal for each of the wavelengths considered.One may for instance average the dx obtained for n acquisitionscorresponding to the following wavelengths according to the formula:$\begin{matrix}{< {x}>=\frac{\sum\limits_{i = 1}^{N}\quad \frac{{dx}_{i}}{\sigma_{i}^{2}}}{\sum\limits_{i = 1}^{N}\quad \frac{1}{\sigma_{i}^{2}}}} & (18)\end{matrix}$

[0090] where σ_(i) ² is defined by the equation (17), for the wavelengthi.

[0091] It is then possible to optimise the measurements of thedielectric function ε pour each wavelength by using this value for thethickness' and by minimising X² by the formula:

X ² =|dS ₁′(ε,<dx>)−dS ₁|² +|dS ₂′(ε,<dx>)−dS ₂|²  (19)

[0092] The method, according to the invention, may also advantageouslybe used in the case of incoherent reflection of a transparent and thicksubstrate by using the equations (3).

[0093] In different particular embodiments having each its ownadvantages and liable to possible combinations, the method, according tothe invention, may adopt the following forms:

[0094] A first particular embodiment considers the case where one of themeasurements dS₁ or dS₂ is unusable for determination of the parametersx, ε. The method, according to the invention, requires indeedsimultaneous measurement of the signals dS₁ and dS₂ in order to obtainthe parameters x, ε of the layers deposited. It may however prove forinstance that the experimental noise is sufficient to make one of bothmeasurements unusable. A solution consists then in developing the termsdS₁ and dS₂ respectively of the equations (12) and (13) to the secondorder as a function of time. This development is allowed since thedevelopment in dx contains terms of the second order. The terms dS₁ anddS₂ can then be written as:

dS _(1,2)(t)=A ^(t) _(1,2) .dt ² +B ^(t) _(1,2) .dt

[0095] where A_(1,2) and B_(1,2) may be determined using theexperimental measurement for the layer being deposited.

[0096] By assuming a constant deposition rate v=dx/dt, the followingequation can be provided:

dS _(1,2)(t)=A ^(t) _(1,2) /v ² .dx ² +B ^(t) _(1,2) /v.dx

[0097] By identifying the factors of this equation with those of theequations (12) and (13) and by eliminating the deposition rate v, a new“master function” may be obtained:

P(ε^(±2))=A ^(t) _(1,2) [Bhd 1,2 (ε^(±1))]² −A _(1,2)(ε^(±2)).[B ^(t)_(1,2)]²=0

[0098] By multiplying this function by ε², one obtains a polynomial oforder 4 whereof the solution, obtained after suitable filtering of theroots of this equation according to the description above, gives ε thendx.

[0099] In a second particular embodiment, it may prove also that thedeposition rate v=dx/dt is not constant during the deposition or thatits value is not known at the beginning of the deposition. There remainsthen to adapt dynamically the value of the reversing pitch so that itsvalue is still optimum for good determination of the parameters x and ε.This dynamic correction procedure of the reversing pitch is based on thecomparison of the values dS_(1,2) with the respective values of theexperimental noise ΔS^(e) and uncertainty bars on the theoretical valuesΔS^(t). As soon as the values of the variations dS_(1,2) measuredbetween the latter point used for the inversion and the new pointrecorded, are greater than γ. Max(ΔS^(e), ΔS^(t)), where γ is a fittingparameter whereof the value determined experimentally ranges between 1.5and 2, whereas the corresponding wavelength is kept for the reversal.

[0100] This criterion is verified independently for S₁ and S₂. If it isverified for both these signals, the digital reversal, according to theinvention, is performed conventionally. If it is verified for only oneof both signals, the ratio dS₁/dS₂ is then calculated. If the latter isclose to 1, the corresponding wavelength is not kept for the reversal,if not, one should refer to the first particular embodiment mentionedabove.

[0101] In a third particular embodiment, one considers the case wherethe film exhibits a low absorption rate. The couple of values S₁, S₂obtained by the reversal method, according to the invention, is in sucha case no more equal to the theoretical value required S₁, S₂. It isthen necessary to include a correction procedure intended to avoiditerative repetition of these errors during successive reversalsequences. If this difference between theoretical and reconstructedvalues is noted dS, one may write close to the correct solution:$\begin{matrix}{{dS}_{1} = {{\frac{\partial S_{1}}{{\partial{Re}}\quad ɛ} \cdot {d{Reɛ}}} + {{\frac{\partial S_{1}}{{\partial{Im}}\quad ɛ} \cdot {d{Im}}}\quad ɛ} + {\frac{\partial S_{1}}{\partial x} \cdot {dx}}}} & (20) \\{{dS}_{2} = {{\frac{\partial S_{2}}{{\partial{Re}}\quad ɛ} \cdot {d{Reɛ}}} + {{\frac{\partial S_{2}}{{\partial{Im}}\quad ɛ} \cdot {d{Im}}}\quad ɛ} + {\frac{\partial S_{2}}{\partial x} \cdot {dx}}}} & (21)\end{matrix}$

[0102] By writing dx=0 and by grouping in the equations (20) and (21)the real and imaginary parts, one may then write:${dS}_{1} = {{{{Re}\left( \frac{\partial S_{1}}{{\partial{Re}}\quad ɛ} \right)} \cdot {d{Reɛ}}} + {{{{Re}\left( \frac{\partial S_{1}}{{\partial{Im}}\quad ɛ} \right)} \cdot {d{Im}}}\quad ɛ}}$${dS}_{2} = {{{{Im}\left( \frac{\partial S_{2}}{{\partial{Re}}\quad ɛ} \right)} \cdot {d{Reɛ}}} + {{{{Im}\left( \frac{\partial S_{2}}{{\partial{Im}}\quad ɛ} \right)} \cdot {d{Im}}}\quad ɛ}}$

[0103] dS₁ and dS₂ being known, it is possible to deduce therefrom thevalue of the correction terms, dreε and dlmε, for ε. One may thendetermine a new value of (S₁, S₂). If the latter still does notcorrespond to the theoretical value required, said procedure is repeateduntil S is minimum.

[0104] In a last particular embodiment, the case where the methodaccording to the invention gives no solution for a given wavelength λ isprocessed. This may be the case, for instance, when calibration errorsare added to the case, already critical, of the reversal realised forpoints where the thickness of the optical phase is close to multi piesof 2λ. To obtain a reasonable value for the index s and thus carry onthe usage of the method, one may resort to the acquisition ofmeasurements for neighbouring wavelengths of λ. If the materialdeposited enables such approximation, one may fit the values of theindex ε obtained for various wavelengths close to λ by a dispersion lawand thus trace the value ε for the wavelength λconsidered.

[0105] The method of the invention has been subject to severalimplementations presented in the following examples underlining thequality of the results obtained:

EXAMPLE 1

[0106] The method has been implemented to calibrate the deposition oflayers made of silicium nitride oxide in a plasma chamber. In a firststage, one has determined the refraction index reconstructed in relationto the time of deposition (FIG. 1), this figure also shows the molecularoxygen flux which has been modified during the deposition. Therefraction index reconstructed has been determined at two differentwavelengths.

[0107] The graphs showing the evolution of the refraction indexreconstructed as a function of time of deposition exhibit similargeneral profile. An initial phase is observed first of all where therefraction index exhibits quick variation of its value to reach aconstant value. This initial phase corresponds to the nucleation phasefor growing a layer of nitride on its own. As soon as the refractionindex has reached a constant value, the molecular oxygen flux isgradually increased until it reaches its maximum value. Starting witht₁=1500 s, i.e. as the molecular oxygen flux enters the chamber, clearcorrelation may be observed between the gradual diminution of the valueof the reflective index and the gradual increase of the molecular oxygenflux. When the molecular oxygen flux has reached the limit value of 3sccm, the reflective index does not vary any longer. The concentrationin molecular oxygen in the chamber is then sufficient to oxide all thesilane molecules.

[0108] From such results, one has attempted to deduce therefrom thevariation of the refraction index averaged over the individual layers(the time of deposition of said individual layers being fixed to 400 s)as a function of the molecular oxygen flux for two wavelengths (FIG. 2).The uncertainties on the mean value of the refractive index of eachlayer have been marked on the figure by error bars. These curves havethen been fitted (solid lines) in order to deduce therefrom for eachwavelength, a curve representing the variations of the refractive indexas a function of the molecular oxygen flux. The growth ratio of theindividual layers has been determined and fitted, similarly.

EXAMPLE 2

[0109] The parameters determined in the example 1 have been used for thedeposition on a glass surface of a layer exhibiting a linear increase ofits refractive index. This stacking should contain, at its upper andlower ends, a layer of high and low index of a thickness 500 Å used as areference index. On FIG. 3, one may observe that the total thicknessreconstructed of the stacking after deposition is 3278 Å. It may benoticed that growth rate exhibits a profile quasi identical to thatrequired, i.e. linear.

[0110] The curves of FIG. 4 correspond to the ellipsometric spectrameasured after said deposition in the energy range 1.5 to 5 eV byvarying the energy of the photons with a pitch of 0.025 eV. These curveshave been modelled and fitted for a spectroscopic model in order toverify the index profile independently of the reversal method. The valueof X² obtained and which measures the quality of the fitting, is 0.46.This value may be considered as excellent, especially for theellipsometric intensity Ic which is, in this particular case, especiallysensitive to the slope of the refractive index profile. The totalthickness obtained by the fitting of the spectra measured, with 3253 Å,matches very well the result obtained by the method according to theinvention, i.e. 3278 Å. The index profile found with such fitting (solidlines) is compared with the results of the method according to theinvention. It can be noted that the value measured for the highestrefractive index is very close to that obtained by the present methodalthough the thickness of the corresponding layer is slightly smaller.Similarly, the index measured for the layer with the lowest refractiveindex is slightly smaller than that obtained by reconstruction. Itshould be noted, however, that the deviations between values obtained byfitting spectra measured and the profiles of reconstruction remain verylow. λ Wavelength k = 2π/λ Wave number S Polarisation perpendicular tothe plane of incidence P Polarisation parallel to the plane of incidenceε Complex dielectric constant N Optical (refraction) index Dx Thicknessof a layer newly deposited on a stacking of layers r_(s) Complexreflection coefficient for polarisation (respectively r_(p))perpendicular (respectively parallel) to the plane of incidence dM_(s)Abeles matrix for a layer of thickness dx and for a (respectivelydM_(p)) polarisation perpendicular (respectively parallel) to the planeof incidence S₁, S₂ Optical signals measured dS₁, dS₂ Variation of theoptical signals measured S₁ and S₂ for a layer of thickness dx newlydeposited ΔS₁, ΔS₂ Experimental errors on the optical signals S₁ and S₂σ² Standard deviation on dS₁, dS₂ between theoretical and experimentalvalues <dx> Average value of the layer of thickness dx for Nacquisitions at different wavelengths λ

1. A characterisation or control method for preparation of a thin layercomponent according to optical methods wherein: parameters S₁ and S₂related to the thickness x and to the complex optical index of thecomponent for a wavelength λ are measured and acquired, the signals S₁and S₂ thus acquired are processed in order to obtain the parameters x,ε of the layers deposited, characterised in that: the stacking isrepresented by the product of two Abeles matrices for each polarisationdirection s (perpendicular to the plane of incidence) and p (parallel tothe plane of incidence) a matrix Mo_(s,p) known representing thesupport, a matrix dM_(s,p) representing a thin transparent layer beingdeposited, the inversion of the variations of the measured signals dS₁,dS₂ enables to get the thickness x and the dielectric constant E of thethin layer using the following operations: Taylor development inrelation to the variation dx of the thickness x of the thin layer of thecoefficients of the matrix dM, calculation of the coefficients of thematrix M_(s,p) each in the form A(ε^(±2))dx²+B(ε^(±1))dx+C deducingtherefrom the relation S_(1,2)=A_(1,2)(ε^(±2))dx²+B_(1,2)(ε^(±1))dx+C_(1,2) linking the signals S₁ and S₂ to the parameters ε and dx,eliminating dx, deducing therefrom a master function P(ε^(±4))=0 solving the equation using an appropriate method, selecting thesolutions of this equation corresponding to values physically plausible,to measure ε, using the value ε obtained to determine dx.
 2. A methodaccording to claim 1, characterised in that the Taylor development islimited to the second order.
 3. A method according to one of the claims1 to 2, characterised in that said method is applied during thedeposition of the stacking and in that the evolution of ε and/or x_(o)is recorded
 4. A method according to one of the claims 1 to 3,characterised in that said method is applied during the deposition ofthe stacking and in that the conditions of the deposition are influencedto interlock the parameters ε, x of the layers with the presettheoretical values.
 5. A method according to claim 1, characterised inthat the ellipsometer is phase-modulated generating the parameters I_(s)and I_(c).
 6. A method according to claim 1, characterised in that theellipsometer is fitted with a rotary polariser generating the parameterstan Ψcos Δ.
 7. A method according to one of the claims 1 to 6,characterised in that the thin layer is transparent.
 8. A methodaccording to one of the claims 1 to 7, characterised in that the thinlayer is absorbent.
 9. Method according to one of the claims 1 to 8,characterised in that the measurement is multiwavelength.
 10. Methodaccording to claim 9, characterised in that the thickness is optimisedby averaging over the different wavelengths.
 11. A method according toclaim 10, characterised in that after optimising the thickness, thecomplex indices are re-calculated.
 12. A method according to any of theclaims 1 to 11, characterised in that, if one of the measured signalsS₁, S₂ is unusable, the other of the terms S1, S2 is developed to thesecond order in relation to time in the relation S₁,S₂=A_(1,2)(ε^(±2))dx²+B_(1,2)(ε^(±1))dx+C_(1,2) in order to determine anew master function P(ε^(±2))=0.
 13. A method according to any of theclaims 1 to 12, characterised in that, if the deposition rate in theinitial conditions of deposition is unknown or is not constant duringthe deposition, the value of the reversing pitch is adapted dynamically.14. A method according to any of the claims 1 to 13, characterised inthat, for a film exhibiting a low absorption rate, attempt is made tominimise the deviation between required and reconstructed theoreticalvalues.
 15. A method according to any of the claims 1 to 14,characterised in that, if no value is obtained for a given wavelength λ,the values of the index ε obtained for various wavelengths close to λare processed to deduce therefrom the value of ε for the wavelength λconsidered.